Journal of Philosophical Logic 41 (5):901-922 (2012)

Maarten McKubre-Jordens
Canterbury University
Zach Weber
University of Otago
This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open
Keywords Paraconsistent logic  Non-classical mathematics  Compactness theorems
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DOI 10.1007/s10992-011-9210-6
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Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.

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Paraconsistent Logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
Transfinite Cardinals in Paraconsistent Set Theory.Zach Weber - 2012 - Review of Symbolic Logic 5 (2):269-293.
Inconsistent Boundaries.Zach Weber & A. J. Cotnoir - 2015 - Synthese 192 (5):1267-1294.
The Relevant Fragment of First Order Logic.Guillermo Badia - 2016 - Review of Symbolic Logic 9 (1):143-166.

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